A New Effective Jackknifing Estimator in the Negative Binomial Regression Model

Abstract

The negative binomial regression model is a widely adopted approach when dealing with dependent variables that consist of non-negative integers or counts. This model serves as an alternative regression technique for addressing issues related to overdispersion in count data. Typically, the maximum likelihood estimator is employed to estimate the parameters of the negative binomial regression model. However, the maximum likelihood estimator can be highly sensitive to multicollinearity, leading to unreliable results. To eliminate the adverse effects of multicollinearity in the negative binomial regression model, we propose the use of a jackknife version of the Kibria–Lukman estimator. In this study, we conducted a theoretical comparison between the proposed jackknife Kibria–Lukman negative binomial regression estimator and several existing estimators documented in the literature. To assess the performance of the proposed estimator, we conducted two simulation studies and performed a real data application. The results from both the simulation studies and the real data application consistently demonstrated that the proposed jackknife Kibria–Lukman negative binomial regression estimator outperforms other estimators.

Keywords

• jackknife Kibria–Lukman estimator
• Kibria–Lukman estimator
• Liu-type estimator
• ridge estimator
• multicollinearity
• negative binomial regression model